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Double Blue Straggler sequences in GCs: the case of NGC 3621

E. Dalessandro2, F. R. Ferraro2, D. Massari2, B. Lanzoni2, P. Miocchi2, G. Beccari3, A.

Bellini4, A. Sills5, S. Sigurdsson6, A. Mucciarelli2, L. Lovisi2

2 Dipartimento di Fisica e Astronomia, Universita degli Studi di Bologna, Viale Berti

Pichat 6/2, I–40127 Bologna, Italy3 European Southern Observatory, Karl Schwarzschild Strasse 2, D-85748, Garching bei

Munchen, Germany4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA5 Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S

4M1, Canada6 Department of Physics and Astrophysics, Pennsylvania State University, 525 Davey

Laboratory,

University Park, Pennsylvania 16802, USA

09 October, 2013

ABSTRACT

We used high-quality images acquired with the WFC3 on board the HST to

probe the blue straggler star (BSS) population of the Galactic globular cluster

NGC 362. We have found two distinct sequences of BSS: this is the second case,

after M 30, where such a feature has been observed. Indeed the BSS location,

their extension in magnitude and color and their radial distribution within the

cluster nicely resemble those observed in M 30, thus suggesting that the same

interpretative scenario can be applied: the red BSS sub-population is generated

by mass transfer binaries, the blue one by collisions. The discovery of four new

W UMa stars, three of which lying along the red-BSS sequence, further supports

this scenario. We also found that the inner portion of the density profile deviates

from a King model and is well reproduced by either a mild power-law (α ∼

−0.2) or a double King profile. This feature supports the hypothesis that the

cluster is currently undergoing the core collapse phase. Moreover, the BSS radial

distribution shows a central peak and monotonically decreases outward without

any evidence of an external rising branch. This evidence is a further indication of

the advanced dynamical age of NGC 362: in fact, together with M 30, NGC 362

belongs to the family of dynamically old clusters (Family III) in the ”dynamical

clock” classification proposed by Ferraro et al. (2012). The observational evidence

presented here strengthens the possible connection between the existence of a

double BSS sequence and a quite advanced dynamical status of the parent cluster.

– 2 –

Subject headings: binaries: general; blue stragglers; globular clusters: individual

(NGC 362)

1. INTRODUCTION

Among the large variety of exotic objects (like X-ray binaries, millisecond pulsars, etc.)

which populate the dense environment of Galactic globular clusters (GGCs; see Bailyn 1995,

Paresce et al. 1992, Bellazzini et al. 1995, Ransom et al. 2005, Pooley & Hut 2006, Freire

et al. 2008), Blue Straggler Stars (BSS) surely represent the most numerous and ubiquitous

population. BSS were observed for the first time in the outer regions of the Galactic GC

M 3 (Sandage 1953). Since then, they have been detected in any properly observed stellar

system (GGCs, see Piotto et al. 2004, Leigh et al. 2007; open clusters – Mathieu & Geller

2009 – dwarf galaxies – Mapelli et al. 2009). BSS are brighter and bluer than the main

sequence turnoff (MSTO), thus mimicking a population significantly younger than normal

cluster stars. Indeed, observations demonstrated that they have masses larger than that of

MSTO stars (m = 1.2 − 1.7 M⊙; Shara et al. 1997; Gilliland et al. 1998; De Marco et

al. 2004). However, stellar evolution models predict that single stars of comparable mass

generated at the epoch of the cluster formation should have already evolved away from the

MS; thus some mechanisms must have been at work to increase the mass of these objects in

their relatively recent past (2− 3 Gyr ago; Sills et al. 2002).

Two main formation scenarios for BSS have been proposed over the years: mass transfer

(MT-BSS) and direct collision (COL-BSS). The collisional formation channel between two

single stars was theorized for the first time by Hills & Day (1976). Following works (Lombardi

et al. 2002; Fregeau et al. 2004) showed that BSS may form also via collision between binary-

single and binary-binary systems. In the mass transfer scenario (McCrea 1964; Zinn & Searle

1976; Leonard 1996), the primary star transfers material to the secondary one through the

inner Lagrangian point when its Roche Lobe is filled. In this picture the secondary star

becomes a more massive MS star (with a lifetime increased by a factor of 2 with respect to a

normal star of the same mass – McCrea 1964) with an envelope rich of gas accreted from the

donor star. Chemical anomalies are expected for MT-BSS (Sarna & De Greve 1996), since

the accreted material (currently settled at the BSS surface) could come from the inner region

1Based on observations collected with the NASA/ESA HST, obtained at the Space Telescope Science

Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. Also based on WFI ob-

servations collected at the European Southern Observatory, La Silla, Chile, within the observing program

07.D-0188.

– 3 –

of the donor star, where nuclear processing occurred. Spectroscopic results supporting the

occurrence of the MT formation channel in a few BSS have been recently obtained (Ferraro

et al. 2006a; Lovisi et al. 2013). Conversely, surface chemical anomalies are not expected

for COL-BSS (Lombardi et al. 1995), since no significant mixing should occur between the

inner core and the outer envelope.

In GCs, where the stellar density significantly varies from the center to the external

regions, BSS can be generated by both processes (Fusi Pecci et al. 1992, Bailyn 1992,

Ferraro et al 1995). Recent works suggested that MT is the dominant formation mechanism

in low density clusters (Sollima et al. 2008) and possibly also in high-density clusters (Knigge

et al. 2009). However the discovery of two distinct sequences of BSS in M 30 (Ferraro et

al. 2009, hereafter F09) clearly separated in color further supports the possibility that both

formation channels can coexist within the cluster core. In fact the blue BSS sequence is

nicely reproduced by collisional models (Sills et al 2009), while the red one is compatible

with binary systems undergoing MT (see Tian et al. 2006). The origin of the double sequence

might be possibly related to the core-collapse process that can trigger the formation of both

red and blue BSS, enhancing the probability of collisions and boosting the mass-transfer

process in relatively close binaries. Given the evolutionary time-scales for stars in the BSS

mass range, the fact that the two sequences are still well distinguishable is a clear indication

that core collapse occurred no more than 1− 2 Gyr ago.

Independently of their formation mechanism, BSS are surely the brightest among the

most massive stars within their host cluster, with a mass that can be even three times larger

than the average stellar mass in old stellar systems (〈m〉 ∼ 0.5M⊙). For this reason they

are ideal tools to probe the dynamical evolution of stellar systems. The radial distribution

of BSS with respect to normal cluster populations (like Horizontal Branch – HB – and Red

Giant Branch – RGB) in GGCs is typically found to be bimodal (see Dalessandro et al. 2008a

and references therein): strongly peaked in the central regions, decreasing at intermediate

distances from the center and rising again in the outskirts. A few exceptions to this general

rule are observed: in ω Centauri (Ferraro et al. 2006b), NGC 2419 (Dalessandro et al.

2008b) and Palomar 14 (Beccari et al. 2011) BSS share the same radial distribution as

the normal cluster stars; instead in a few other cases such as M 80 (Ferraro et al. 1999a;

Ferraro et al. 2012, hereafter F12), M 79 (Lanzoni et al. 2007a), M 75 (Contreras Ramos

et al. 2012) and M 30 (F09, F12), the BSS distribution is monotonic, with a high peak in

the innermost regions and rapidly declining outward with no signs of rising branch. Simple

Monte Carlo simulations (Mapelli et al. 2004, 2006) have shown that the observed radial

distribution of BSS is reproduced by assuming that both formation processes are active, with

COL-BSS contributing only to the central peak, and MT-BSS being necessary to account

for the external rising branch. More recently F12 suggested that the BSS radial distribution

– 4 –

can be used as a powerful indicator of the cluster dynamical age (the dynamical clock).

In this picture, GCs with a flat BSS distribution are quite young stellar systems, clusters

with a centrally peaked and monotonically decreasing BSS distribution are dynamically old,

and those showing a bimodal distribution have intermediate dynamical ages (their degree

of dynamical aging being a function of the radial position of the minimum in the BSS

distribution). In this context M 30 belongs to the family of dynamically old GCs, in very

good agreement with its status of post core-collapsed cluster suggested by the shape of its

density profile and with the proposed interpretation of its double BSS sequence (F09).

In order to further explore the link between the presence of a double sequence of BSS

and the occurrence of core collapse, we acquired Hubble Space telescope (HST) images with

the Wide Field Camera 3 (WFC3) for a sample of suspected post-core collapse GGCs. Here

we present the first results of this project and we report on the discovery of the second case

of a BSS double sequence, in NGC 362. The paper is structured as follows: in Section 2 we

present the data-base and we describe the photometric analysis, as well as the calibration and

astrometry procedures adopted. In Section 3 the determination of the center and density

profile is described and a comparison with previous studies about the dynamical state of

NGC 362 is performed. In Section 4 we briefly discuss the relative proper motion analysis

adopted to ”clean” the BSS sample from contaminating field stars and in Section 5 we go

in detail about the detection of the BSS double sequence and its comparison with M 30.

Finally in Section 6 we discuss our main results.

2. OBSERVATIONS AND DATA ANALYSIS

In the present work we used data acquired with the UVIS channel of the WFC3 on

2012 April 13 (Proposal ID: 12516; PI: Ferraro). The WFC3/UVIS camera consists of two

twin chips, each of 4096 × 2051 pixels, separated by a gap of approximately 30 pixels. The

pixel scale is 0.04′′ pixel−1, therefore the resulting Field of View (FoV) is 162′′ × 162′′. The

cluster is approximately centered on chip# 1 (Figures 1 and 2). The dataset is composed

of fourteen exposures obtained through the F390W (hereafter U2) filter, each one with an

exposure time texp = 348 sec, ten F555W (V) images with texp = 150 sec and fifteen F814W

(I) frames with texp = 348 sec. Each pointing is dithered by a few pixels in order to allow a

better subtraction of CCD defects, artifacts and false detections. For the analysis we used

the set of images processed, flat-fielded and bias subtracted by standard HST pipelines ( flt

2Although the F390W filter almost corresponds to the broad filter C of the Washington photometric

system (Canterna 1976), we prefer to label it “U filter” since it is more popular.

– 5 –

images). The data reduction has been performed independently on each exposure by using

the publicly available point spread function (PSF) fitting software img2xym wfc3uv, which

is mostly based on img2xym WFC (Anderson et al. 2008). Pixel-area effects have been applied

to the derived fluxes and geometric distortions have been corrected by using the geometric

distortion solution provided by Bellini et al. (2011).

For each photometric band, the obtained star lists have been combined in order to create

a filter master catalog (FMC), consisting of stars measured in at least five different frames.

For each star, different magnitude estimates have been homogenized (see Ferraro et al 1991,

1992) and their weighted mean and standard deviation have been finally adopted as the

star magnitude and its photometric error. We then combined the three FMCs to create the

final star list, requiring that a star is present in at least 2 FMCs (i.e. it has two measured

magnitudes).

Instrumental magnitudes have been reported to the VEGAMAG photometric system

by adopting the zero points reported in the WFC3 web page3 for a 0.4′′ aperture correction.

Stars with I< 16.5 suffer from non-linear CCD response and saturation problems; thus they

were not considered for the BSS analysis. The analysis of the BSS double sequence has been

performed by using exclusively WFC3 data (see Section 5.1) Instead additional HST and

ground-based observations have been considered for the determination of the cluster center,

to build the star-count density profile all over the entire radial extension of the cluster and

to study the BSS radial distribution. In particular, we used images obtained with the Wide

Field Imager (WFI) mounted at the MPG/ESO 2.2m telescope. The WFI frames consists

of eight 4096 × 2048 pixel chips with a spatial resolution of 0.228′′ pixel−1, thus each WFI

exposure covers a FoV of about 33′ × 34′.

We used 5 long exposures (Prop: 07.D-0188(A); PI: Ortolani), two obtained through the

B band with texp = 360 sec each, and three in V band with texp = 300 sec. We also used

two short exposures, one B and one V, with texp = 20 sec each, to properly measure the

bright portion of the RGB and Asymptotic Giant Branch sequences. Master bias and flat-

fields have been obtained by using a large number of calibration frames. Scientific images

have been corrected for bias and flat-field by using standard procedures and tasks contained

in the Image Reduction and Analysis Facility (IRAF)4. The photometric analysis has been

performed on each chip separately by using DAOPHOTII (Stetson 1987). For each frame we

selected several tens of bright and relatively isolated stars to model the PSF. We used a

3http://www.stsci.edu/hst/wfc3/phot zp lbn

4IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Associ-

ation of Universities fro Research in Astronomy, Inc., under the cooperative agreement with the National

Science Foundation.

– 6 –

Moffat analytic function and a first order spatial variation for the PSF. For each chip we

obtained a star list that was then combined by using DAOMATCH and DAOMASTER. Only stars

measured at least twice in each band were considered. We used the B and V magnitudes of the

Stetson photometric secondary standard catalog (Stetson 2000) to report our instrumental

magnitudes Bins and Vins to the standard Johnson photometric system. In particular, we

analyzed the distributions in the (B − Bins, Bins − Vins) and (V − Vins, Bins − Vins) planes

for the stars in common, and we used their best-fit relations to calibrate the instrumental

magnitudes. We adopted as calibration relations the linear best fits to the two distributions.

The WFI data have been used to obtain the density profile in the external regions (see

Section 3) and the BSS radial distribution in the area not covered by the WFC3 data-set.

(Section 5.3).

In the innermost, highly-crowded regions we exploited also the high spatial resolution of

the Advanced Camera for Survey (ACS) High Resolution Channel (HRC). The HRC is a

1024× 1024 pixels array with a pixel scale of ∼ 0.026′′/pixels, thus covering a FoV of about

28′′ × 25′′. The HRC data-set (Prop ID=10401; PI: Chandar) consists of eleven exposures

of 85 sec each obtained with the broadband filter F435W (∼ B). As for the WFC3 data-set,

we used flt images pre-processed by the standard HST pipelines. Each exposure has been

corrected for pixel area effect, by using the most-updated Pixel Area Map images available

at the HST web site. The analysis has been performed in each frame independently by using

DAOPHOTII and by selecting some tens of stars to model the PSF. Also in this case we adopted

a Moffat analytic PSF and a first order variation. Star positions and magnitudes have been

then combined with DAOMATCH and DAOMASTER. Instrumental magnitudes have been reported

to the VEGAMAG photometric system by using the prescriptions and zero points listed in

the ”ACS Calibration and Zeropoints” web page5. The HRC data have been crucial for an

accurate determination of the cluster center and to provide a complete sample of stars to

built the star-count density profile in the innermost few arcsec (Section 3).

The instrumental positions of stars in each WFI chip have been separately roto-translated

to the absolute (α, δ) coordinates by using the stars in common with the astrometric stan-

dards listed in the Guide Source Catalogue 2.3 (GSC2.3) and the cross-correlation software

CataXcorr. For each chip we found several tens of stars in common (hundreds in the chip

containing the cluster core) thus allowing a very accurate roto-translation solution. Once all

the chips were put on the absolute coordinate system, we merged them in a single homoge-

neous source catalogue. We then used the stars detected with WFI and falling in the WFC3

FoV as secondary astrometric standards. In this case several thousands of stars have been

found in common. Similarly, positions of stars detected with HRC were first corrected for

5http://www.stsci.edu/hst/acs/analysis/zeropoints

– 7 –

geometric distortions and then put on the absolute reference system by using the stars in

common with the WFC3 catalog.

At the end of the procedure we have three independent star catalogues on the same

coordinate reference system. As anticipated they have been all used for building the density

profile (see Section 3) and to determine the center of gravity, while we used only the WFC3

star list to study the BSS population.

3. Determination of the cluster center and density profile

The dynamical state of NGC 362 is quite uncertain. A detailed study has been performed

by Fischer et al. (1993), who combined photometric data and radial velocities for ∼ 200

RGB stars. By using single- and multi-mass King-Michie (KM) models they were able to

reproduce well the surface brightness profile (SBP) of this system. However the observational

constraints from the kinematics and rotation obtained with the spectroscopic data were not

compatible with the best-fit KM models in the assumption of isotropy. In order to reconcile

the kinematical measures with the observed SBP a shallow mass function and intermediate

amounts of anisotropy in the velocity-dispersion tensor had to be adopted. On the basis of

SBP fitting, this cluster has been classified as a possible PCC by Trager et al. (1995; their

best fit structural parameters are c = 1.94 and rc = 10.2′′). Also Harris (1996, version 2010)

classified this system as possible PCC (c = 1.76, rc = 10.8′′), while McLaughlin & van der

Marel (2005) were able to reproduce its SBP with a King model with parameters c = 1.80,

rc = 10.1′′ without discussing the possibility that this system already underwent the collapse

of the core.

In order to clarify the complex picture of the dynamical state of NGC 362, we used the

entire data-set described in Section 2 to obtain its surface density profile from resolved star

counts. First we determined the center (Cgrav) of NGC 362, by averaging the positions α and

δ of selected stars lying in the HRC FoV (see for example Ferraro et al. 2003a; Dalessandro

et al. 2009). We preferred to use the HRC data because of the many saturated stars in the

inner regions of the cluster present in WFC3 images, and because of the higher resolution of

the HRC camera. This choice however limits the distance from the center within which we

can average the positions of stars. We chose the center listed by Goldsbury et al. (2010) as

starting guess point of our iterative procedure (Montegriffo et al. 1995). In order to avoid

spurious or incompleteness effects, we performed different measures averaging the position

of stars selected in different magnitude intervals6 (all within the range 12.5 <V< 18.5) and

6Note that for the HRC sample, the limits in V have been inferred by using the stars in common with

– 8 –

distance (d) from the starting guess center (8′′ < d < 12′′). The resulting Cgrav is the average

of these measures and it is located at αJ2000 = 01h : 03m : 14s.099, δJ2000 = −70◦ : 50′ : 56′′.04

(RA = 15.8087453, Dec = −70.8489012). The estimated Cgrav turns out to be at a distance

d ∼ 0.90′′ (corresponding to ∼ 1σ of our measures) in the South-West direction from the

one listed by Goldsbury et al. (2010).

By properly combining the HRC, WFC3 and WFI data-sets, we constructed the density

profile by using direct star counts along the entire radial extension of the cluster. As shown

in Figure 3, we typically used stars in the magnitude range 17.5 <V< 19.5 in order to avoid

incompleteness and saturated stars. When possible, however, as in the case of the HRC

sample, which does not show saturation problems, we extended our selection to stars brighter

than this limit. We sub-divided the total FoV in 30 concentric annuli centered on Cgrav and

reaching r = 1300′′. For r < 16′′ we used only stars in the HRC FoV, for 16′′ < r < 100′′ stars

in the WFC3 FoV and for the outer regions we used the WFI catalog. Each annulus was then

split in an adequate number of sub-sectors (2 or 4 depending on the number of stars). In each

sub-sector the density has been estimated as the ratio between the selected number of stars

counted and the covered area. The density assigned to a given annulus is the average of the

densities of each sub-sector of that annulus. Densities thus obtained have been corrected for

incomplete area coverage due to the WFI gaps. The error assigned to each density measure

is defined as the dispersion from the mean of the sub-sector densities. Overlapping annuli

were used to check and apply normalizations between the three subsamples. The resulting

density profile is shown in Figure 4 (open squares). As clearly visible in the right panel of

Figure 3, NGC 362 is contaminated by fore- and back-ground Galaxy stars and even more

strongly by stars belonging to the Small Magellanic Clouds (SMC; see the population at

(B − V ) ∼ 0 and (B − V ) > 0.6, respectively). We estimated the background density by

using the six outermost points (with distances from Cgrav r > 450′′), that have almost the

same density, describing a sort of plateau 7. We subtracted the mean background value to all

the other annuli and the resulting density profile is shown in Figure 4 (black filled circles).

As expected, after the background correction, the profile changes sensibly in the outermost

regions, while it remains unchanged in the innermost ones.

We performed a fit of the density profile by using a single-mass King model (King 1966).

We excluded from the fit the three innermost points (r < 3′′) of the observed profile, since

WFC3 catalog (see leftmost panel of Figure 3).

7For the most distant annulus (1000′′ < r < 1300′′), variations are observed as a function of the azimuthal

angle in which the density is calculated. In particular the density is slightly larger toward the SMC direction

(even if this discrepancy has not a high statistical significance). However this effect has a negligible impact

on the overall background determination.

– 9 –

they appear to deviate from a flat core behavior (see the inset in Figure 4). The best fit

model is obtained for a core radius rc = 13′′, concentration c = 1.74 and limiting radius

rt ∼ 720′′. The parameters obtained from our analysis are slightly different from those

obtained in previous works (in particular, rc is about 30% larger, while c is up to 15%

smaller). However our estimates cannot be directly compared with previous determinations

because they included also the innermost 3′′ (which are instead excluded in our analysis).

The innermost portion of the observed density profile (r < 3′′) is well fitted by a mild power-

law with slope α ∼ −0.2. The derived power-law is shallower than what typically observed

(and expected) for post core-collapse clusters (for example α ∼ −0.5 for M 30; F09). It

is worth noting, however, that N-body simulations (Vesperini & Trenti 2010) show that

the presence of relatively shallow cusps in the density and SBPs could be found in clusters

during the phase of either pre-core-collapse or core-collapse. On this basis we can argue that

NGC 362 is possibly experiencing the core-collapse event.

We also tried to fit the innermost portion of the profile with an additional King model, as

done by Ferraro et al. (2003b) for the case of NGC 6752. In particular we found that for

r < 3′′ the profile is well fit by a King model with c = 2.9 and rc = 4.7′′ (see inset in

Figure 4). Also this behavior would suggest that NGC 362 is a post core-collapse cluster

experiencing a post-core-collapse bounce, i.e. a large amplitude oscillation in the core due to

gravothermal instability of collisional systems (Cohn et al. 1991). We also tried to reproduce

the entire surface density profile with multi-mass King models, but the fit always resulted

of significantly lower quality with respect to the best solution described above.8

4. Proper motion analysis

As evident in Figure 5 and as already discussed in previous Section 3, the CMD of

NGC 362 is contaminated by fore and background Galaxy stars and even more strongly

by the SMC populations. In particular the MS of the SMC defines a quite clear sequence

at V > 20 and 0 < (U − I) < 2. In order to evaluate the level of contamination in the

direction of the cluster, we performed a relative proper motion analysis. For this purpose we

complemented our HST WFC3 images with a first epoch data-set consisting of Wide Field

Camera ACS images obtained in June 2006 (Prop ID 10775; PI: Sarajedini). The proper

motion analysis has been performed following the approach described in Anderson et al.

(2010). Briefly, the procedure consists in measuring the displacement of the instrumental

8A mono-mass King model with the same structural parameters but including a central IMBH (Miocchi

2007) with MIMBH/Mcluster = 3× 10−3 is able to reproduce the innermost 3′′ of the observed profile better

than the multi-mass models.

– 10 –

(x, y) coordinates between the positions of stars in the first epoch and the corresponding

positions in the second one, once a common reference frame is defined. The first step is to

adopt a distortion-free reference frame. The ideal choice was to adopt as reference frame the

one published by Anderson et al. (2008). The second step is to find accurate transformations

between each single-frame catalogue and the reference frame. In order to do that, we strictly

selected unsaturated stars with magnitude ranging between 18 < mag < 21 in each band.

Moreover, we selected only stars distributed along the MS and the sub-giant branch (SGB)

of NGC 362, in order to derive global 6-parameters linear transformations by using stars

with a high probability to be cluster members. For this selected sample of stars (hereafter

the reference stars) the residuals of the transformations are always smaller than 0.03 pixels

(which accounts for measurement errors and stars’ internal motion). We then applied the

derived transformations to all the stars detected in each frame. Every single-frame catalogue

coordinate (x, y) has been transformed onto the distortion free reference exposure. We will

refer to this transformed coordinate as (xt, yt). The mean position of a single star in each

epoch (xm, ym) has been measured as the 3-sigma clipped mean position calculated among

all the N individual single-frame measurement (xt, yt), and the relative r.m.s. of the position

residuals around the mean value divided by√

(N) has been used as associated error (σ).

Finally, displacements are obtained as the difference of the positions (xm, ym) between the

two epochs for all the stars in common. The error associated to the displacement is the

combination of the errors on the positions of the two epochs. We iteratively repeated the

procedure, by rejecting from the initial list of reference cluster stars those whose motion

was not consistent with the cluster mean motion, and we re-calculated new, improved linear

transformations. Thus, according to the procedure described above, only stars with residuals

(σX = |xt − xm| and σY = |yt − ym|) smaller than 0.8 pixels were considered after each

iteration. The convergence is assumed when the number of reference stars that undergoes

this selection changes less than the 5% between two subsequent steps. The displacements

obtained with this approach are converted in relative proper motions, measured in pixel yr−1

(here the pixel is that of the reference frame 0.05′′ pixel−1), by dividing for the temporal

baseline (∼ 5 yr).

The upper panels of Figure 5 present the vector point diagram (VPD), where we can

distinguish two main sub-populations. The first and dominant one, centered at (µX = 0

pixel yr−1, µY = 0 pixel yr−1) is, by construction, the cluster population. The second, at

(µX = 0.7 pixel yr−1, µY = 0.2 pixel yr−1) is instead populated by the SMC stars. The

separation between the two components appears clearly in the (V,U-I) CMDs as shown in

the lower panels of Figure 5. In Figure 6, we show the VPD at different magnitude levels.

As expected, the population belonging to the SMC starts to appear in the VPD diagram

for V > 20. In addition the distribution of NGC 362 and SMC gets broader as a function

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of increasing magnitudes, because of the increasing uncertainties on the centroid positions

of faint stars. The same behavior is visible at bright magnitudes (V < 17) because of

non-linearity and saturation problems.

To build a clean sample of stars with a high membership probability, we defined in the

VPD and for each magnitude bin a different fiducial region centered on (µX = 0 pixel yr−1,

µY = 0 pixel yr−1). The fiducial regions have radii of 2 × σ, where σ is the dispersion of

fiducial member stars, i.e. those with a distance r < 0.3 pixel yr−1 from (µX = 0 pixel yr−1,

µY = 0 pixel yr−1) (see the member selection in the upper panels of Figure 5). It is worth

noting that slightly different criteria for the membership selection do not appreciably affect

the results about the BSS population.

5. The BSS population

5.1. The BSS double sequence

The evidence shown in Section 3 suggests that NGC 362 could have started the core col-

lapse process. This makes it particularly interesting in the context of the working hypothesis

proposed by F09 that clusters undergoing the core-collapse process could develop a double

BSS sequence. For this reason, the BSS population of NGC 362 has been analyzed first in

the (V,V-I) CMD, in order to perform a direct comparison with the observations of M 30

(F09). Following the approach adopted in previous papers (Lanzoni et al. 2007b; Dalessan-

dro et al. 2008b) we selected BSS candidates by defining a box which roughly selects stars

brighter and bluer than the TO point, corresponding to VTO ∼ 19 and (V − I)TO ∼ 0.7. As

usual, in our selection we tried to avoid possible contamination of blends from the SGB, TO

region, and the saturation limit of the deep exposures (dashed line in Figure 6). With these

limits 65 candidates BSS have been identified. We emphasize that the selection criteria are

not a critical issue here, since the inclusion or exclusion of a few stars does not affect in any

way the results of the paper. The selected BSS are shown in the zoomed region of the CMD

in Figure 7. At a close look it is possible to distinguish two almost parallel and similarly

populated sequences, separated by about ∆V ∼ 0.4 and ∆(V − I) ∼ 0.15. Such a feature

resembles the one observed in M 30.

In order to perform a more direct comparison with M 30, we over-plotted two fiducial

areas (grey regions in Figure 7) representative of the color and magnitude distribution of the

red and blue BSS populations in that cluster. Differences in distance moduli and reddening

have been properly taken into account. Figure 7 shows that the BSS of NGC 362 nicely fall

within the fiducial regions and only sparsely populate the region between the two. Moreover

– 12 –

the BSS population of NGC 362 show luminosity and color extensions similar to the ones

observed in M 30. The red sequence appears slightly more scattered than that observed in

M 30. This is mainly due to the fact that in the case of NGC 362 a few candidate BSS at

(V − I) ∼ 0.6 have been included into the sample. However, we can safely conclude that,

within the photometric uncertainties, the two BSS sequences of NGC 362 well resemble

the red and blue BSS sequences of M 30. The blue BSS sample counts 30 stars which are

distributed along a narrow and well defined sequence in the (V, V-I) CMD, while the red

sequence counts 35 stars. The relative sizes of the two populations is very similar to what

found in M 30.

We also analyzed the distribution in color and magnitude of the red and blue sequences of

both clusters by comparing their geometrical distance (d) from the same straight line fitting

the blue sequence of M 30 used by F09. To do so, we anchored the two (V, V-I) CMDs at the

TO level of M 30 by correcting for relative differences of reddening and distance moduli. The

result is shown in the upper panel of Figure 8 as an histogram. It reveals the presence of two

distinct peaks nicely overlapping with those observed in M 30, with a separation ∆d ∼ 0.12.

However, both the blue BSS and the red BSS distributions of NGC 362 are broader than

those in M 30; in particular the red sequence is more spread out by ∼ 0.05− 0.1 mag with

respect to the one studied by F09. The bimodality remains clearly visible in the cumulative

histogram shown in the lower panel of Figure 8. In order to quantify the significance of the

bi-modality of the distribution shown in Figure 8, we used the Gaussian mixture modeling

algorithm presented by Muratov & Gnedin (2010). This algorithm evaluates whether a

bimodal fit is an improvement over a unimodal one by performing a parametric bootstrap

and using three different statistics: the separations of the means relative to their widths as

defined by Ashman et la (1994), the kurtosis of the distribution, and the likelihood ratio test

(Wolfe 1971). We obtain that a unimodal distribution is rejected with a 99.6% probability;

hence the distribution shown in Figure 8 is bimodal with a confidence level of 3σ.

We analyzed the spatial distribution of the red and blue BSS populations. Their relative

location in the WFC3 FoV is shown in Figure 2. From this map it is already possible to make

some qualitative considerations: 1) red BSS appear more centrally concentrated than blue

BSS, 2) almost the entire BSS population lies in chip#1. We analyzed in further detail this

fact by looking at the cumulative radial distribution. We used SGB stars in the magnitude

interval 18 <V< 18.5 as reference population. Both the red and the blue BSS samples are

more centrally concentrated than the reference population. A Kolmogorov-Smirnov test gives

a probability P ∼ 10−5 that they are extracted from the same parent population. Moreover,

red BSS are more centrally segregated than the blue ones, with a high (3σ) confidence level

that they are extracted from different populations. In addition, in striking agreement with

what found by F09 in M 30, we do not observe any blue BSS within 5′′ − 6′′ from Cgrav and

– 13 –

both the blue and red samples completely disappear (within the WFC3 FoV) at distances

r > 75′′. The observational evidence collected so far leads us to conclude that NGC 362 is

the second cluster, after M 30, showing a clear double sequence of BSS.

5.2. Variable stars in the BSS sample

The work by Szekely et al. (2007) has strongly contributed to the study of variable stars

in NGC 362. They have increased by three times the number of known variables in this GC.

They found that NGC 362 hosts a relatively large number of variable stars. In particular

they counted 45 RR Lyrae stars and 21 other short-period variables (like δ Scuti, eclipsing

variables, etc.).

With the aim of identifying variables in the selected BSS population, and in order

to avoid contamination from back- and fore-ground variables, in particular from the many

Cepheids and long-period variables belonging to SMC and lying in the BSS region (see Figure

13 in Szekely et al. 2007), we cross-correlated the publicly available list of non-RR Lyrae

short-period variables with our proper motion-cleaned-catalog (see Section 4). In our FoV

we find two stars in common. Both are SX-Phoenicis, as expected for stars crossing the

instability strip at the BSS magnitude level. In the list of Szekely et al. (2007) they are

named V52 and V63 and they have no period determination. In particular V63 exhibits

complex multi-periodic variations. Both V52 and V63 (opens squares in Figures 7 and 15)

fall in the red BSS sequence. The analysis by Szekely et al. (2007) is based on ground-based

data-sets. Thus their work is limited by the relatively poor spatial resolution at least in

the most central and crowded regions. For this reason, taking advantage of the outstanding

capabilities of HST and the relatively large number of images acquired, we performed a

variability search analysis for the selected BSS. Our analysis can identify only stars with

a relatively short period (∼ 10 hours), because of the the time interval covered by our

observations. The identification of variable stars was carried out using the U, V and I time-

series data separately. As a first step, we checked the light curves of the selected BSS visually.

We considered only those stars showing coherent evidences of variability in all the bands.

With this criterion we selected nine stars, two of them being the two SX-Phoenicis identified

by Szekely et al. (2007), the other seven being new variables.

We analyzed the light curves of these seven candidate variable BSS by using the Graph-

ical Analyzer of Time Series (GRATIS), a private software developed at the Bologna Ob-

servatory by P. Montegriffo. GRATIS uses both the Lomb periodogram (Lomb 1976) and

the best fit of the data with a truncated Fourier series (Barning 1963). The final periods

adopted to fold the light curves are those that minimize the rms scatter of the truncated

– 14 –

Fourier series that best fit the data. We emphasize that these are newly discovered candidate

variables. No counterpart for these stars can be found in literature.

Four candidate new variables show in all bands a variability of ∼ 0.3 mag, a value

several times larger than their typical photometric errors, (see Figure 7). Periods of the

order of fraction of days (between 0.15 and 0.30 days) have been estimated with GRATIS.

Such periods, coupled with the light modulation of these stars (Figure 10), would suggest

that these candidates are not pulsational variables but double systems. In particular they

are likely WUMa stars, i.e. semi-detached binaries with ongoing mass-transfer. We named

them CWUMa. These objects are expected to be quite common within the BSS population.

It is worth noting that, out of four candidates WUMa, three lie along the red sequence: they

are CWUMa1, CWUMa2 and CWUMa4.

The remaining three candidate variables have instead much shorter periods, of the order

of P∼ 0.04 − 0.07 days, and their light modulation has amplitudes of about 0.05-0.1 mag.

Their periods and light curves (shown in Figure 11) are typical of SX-Phoenicis stars. We

labeled these stars as CSX. CSX1 and CSX2 are red BSS, while CSX3 is a blue BSS. Their

position in the CMD is highlighted by open pentagons in Figures 7 and 16. With the inclusion

of these three variables, the number of known candidate SX-Phoenicis in NGC 362 increases

from two to five.

5.3. The BSS radial distribution

The BSS radial distribution has been found to be a powerful tool to estimate the dy-

namical age of stellar systems (F12). In fact due to their mass (significantly larger the

average) and to their relatively high luminosity, BSS are the ideal class of object to measure

the effect of dynamical processes (like dynamical friction and mass segregation) from which

the dynamical age of a stellar system can be derived.

By combining the WFC3 and the WFI data, we have been able to study the BSS ra-

dial distribution of NGC 362 along its entire extension. In the complementary WFI catalog

(r > 100′′) the BSS selection has been performed in the (V, B-V) plane by adopting the same

magnitude limits used for the WFC3 catalog (approximately 16.5 <V< 18.5; see Figure 12).

We thus counted 28 BSS within the tidal radius (rt ∼ 720′′; see Section 3). The photometric

accuracy and field star contamination of the WFI catalog do not allow us to investigate the

presence of a double sequence in the cluster peripheries. Therefore, we will consider BSS as

a single population in the following analysis.

In order to have a reference population to study the BSS radial distribution, we selected

– 15 –

bona-fide SGB stars in the magnitude interval 18 <V< 18.5, as done for the WFC3 catalog.

We have already shown, by means of a cumulative radial distribution (Figure 9), that BSS

in the WFC3 FoV are more centrally concentrated than the reference stars. Now we extend

the analysis out to rt and we use the specific frequency NBSS/NSGB. We divided the FoV

in five concentric annuli centered on Cgrav and in each of them we counted the number of

BSS and that of the reference population stars. We estimated the impact of contamination

on the derived number counts by counting the number of stars falling in the BSS and SGB

selection boxes in a reference field beyond the cluster limit, at r > 900′′ from Cgrav (right

panel of Figure 12). The resulting density of contaminating field stars for both the BSS

and the SGB populations is ρ ∼ 0.03 stars/arcmin2. We then used this value to correct the

number counts previously obtained in the five radial bins. As shown in Figure 13, the radial

distribution of NBSS/NSGB is monotonic: highly peaked in the innermost region and rapidly

decreasing outward.

We also computed the double normalized ratio (Rpop) for BSS and SGB, as defined in Ferraro

et al. (1993). For each radial bin, the sampled luminosities have been calculated from the

density profile (Section 3). For the central region (r < 3′′) we used the best-fit slope shown

in Figure 4, instead of a flat core. The value of RSGB is essentially constant with a value

close to the unity (see lower panel of Figure 13), as expected for post-MS stars (Renzini &

Buzzoni 1986). Conversely, the central value of RBSS is ∼ 2, indicating that in the cluster

core BSS are twice more abundant than the reference population (which scales as the cluster

sampled luminosity). Moreover, RBSS monotonically declines for increasing distance from

the center, reaching values close to ∼ 0.4 in the most external annulus, with no evidence of

any external rising branch.

In the context of the ”dynamical clock” discussed in F12, the observed trend of RBSS clearly

places NGC 362 in the group of dynamically old clusters (Family III). Indeed, the compar-

ison shown in Figure 14 fully confirms that the radial behavior of RBSS is very similar to

that of other clusters (M 75, M 80, M 79 and M 30) showing the highest level of dynamical

evolution, with even the most external BSS already sunk toward the cluster center. It is

worth noting that M 30, which is the only PCC cluster in the F12 sample, belongs to this

group.

Additional clues about relative dynamical-age differences within the clusters belonging to

this family can be obtained from the detailed comparison of the BSS radial distribution

shape. In fact, because of its relatively flat decreasing branch, NGC 362 appears to be sim-

ilar to M 75 and M 79, which are the youngest systems in this family. Moreover NGC 362

shows the smallest peak value of RBSS within Family III, again suggesting that it is among

the dynamically youngest clusters within this group.

In order to quantify this impression, we determined the position of NGC 362 in the ”dy-

namical clock” plane (see Figure 4 in F12), where the position of the minimum of the BSS

– 16 –

radial distribution in units of the cluster core radius, log(rmin/rc), is plotted as a function

of the core relaxation time in units of the Hubble time, log(trc/tH). As discussed in F12,

log(rmin/rc) is the time-hand of the dynamical clock. For clusters in Family III, where no

minimum can be detected, F12 assumed as rmin the radius of the most distant bin in the

observed BSS radial distribution. In the case of NGC 362, this distance corresponds to

log(rmin/rc) ∼ 1.6. The core relaxation-time can be derived by using equation (10) in Djor-

govski (1993) and by assuming the structural parameters obtained in Section 3, the distance

modulus and reddening adopted in Section 5.1, and a mass-to-light ratio M/LV = 3 (see

Dalessandro et al. 2013 for more details). We thus obtained that the central relaxation time,

once normalized to the Universe age (tH = 13.7 Gyr) is log(trc/tH) ∼ −2. Figure 15 shows

the position of NGC 362 in the dynamical clock plane. As expected, the cluster lies close to

M 75 and M 79 (showing a strikingly similar BSS radial distribution) and it is among the

youngest systems of this family.

6. Discussion

The accurate HST WFC3 photometry presented in this paper has revealed the presence

of two almost parallel BSS sequences in the core of NGC 362. This represents the second

case, after M 30 (F09), for which a double BSS sequence has been observed. The red and blue

BSS populations are well separated in the (V, V-I) CMD by ∆V∼ 0.4 and ∆(V-I)∼ 0.15,

and they nicely overlap with the distribution of BSS shown in F09 (see Figures 7, 8). As

in the case of M 30, the red population is significantly more centrally concentrated than

the blue one (Figure 9) and their sizes are very similar. Also the total number of BSS

normalized to the total cluster luminosity is basically the same in these two systems. In

fact we count, within rt and after field stars subtraction, 77 BSS in NGC 362 which has

LV ∼ 2 × 105L⊙, and 51 in M 30 (F09) which has instead LV ∼ 105L⊙. F09 argued that

blue BSS are likely the result of collisions while red BSS are binary systems in an active

phase of mass-transfer. Observational hints supporting this interpretative scenario have

been recently shown by Lovisi et al. (2013). A similar approach can be followed to interpret

the two sequences in NGC 362. The results are shown in Figure 16. Indeed the position

of the blue sequence in the CMD can be nicely reproduced by a collisional isochrone (Sills

et al. 2009) of proper metallicity ([Fe/H]=-1.31) and age t = 0.2 Gyr and by assuming a

distance modulus (m−M)0 = 14.68 and reddening E(B−V ) = 0.05 (Ferraro et al. 1999b).

Additional support to the collisional origin of the blue sequence can be obtained from star

counts. In fact the number of expected BSS produced by collisions can be estimated from

– 17 –

equation (4) in Davies, Piotto & de Angeli 2004 (see also Leonard et al. 1989):

NCOL−BSS = 0.03225f 2mmsNcnc,5rcolmBSS

Vrel

(1)

where fmms is the fraction of massive MS stars (i.e. stars able to form a BSS when they

collide) in the core (we assumed here fmms = 0.25; Davies & Benz 1995), Nc is the total

number of stars in the core and nc,5 is the density of stars expressed in units of 105 stars

pc−3 (we adopted nc,5 ∼ 2; Harris 1996), mBSS is the typical BSS mass (we used mBSS =

1.2M⊙), rcol is the minimum separation of the two colliding stars in solar units (we adopted

rcol = 2R⊙), and Vrel is the relative incoming velocity of binaries at infinity (we adopted

Vrel = σ√

(2) from Leonard et al. 1989 and the central velocity dispersion σ from Harris

1996). By using equation (1) and the quoted assumptions, we obtained that about 25 BSS

are expected to be formed in the last 0.2 Gyr by collisions. This is in nice agreement with

the observed number of BSS (30) on the blue sequence. While the blue BSS are all observed

in the WFC3 FOV, equation (1) in principle concerns the entire cluster, since it is based

on the assumption that COL-BSS are formed in the core and then spread out because of

dynamical interactions. However, it is more likely to observe COL-BSS in the inner regions

of stellar systems, than in the outskirts. This is also confirmed by the findings of Mapelli et

al. (2004, 2006) showing that most of the COL-BSS kicked out from the core either leave

the clusters, or sink back rapidly in the core. Hence, the fraction of COL-BSS outside the

WFC3 FOV should be negligible.

In F09 the position of the red BSS sequence in the CMD has been found to be well

reproduced by the lower luminosity boundary defined by the distribution of binary stars

with ongoing mass-transfer, as found in Monte Carlo simulations by Tian et al. (2006). This

boundary approximately corresponds to the locus defined by the Zero-Age-MS (ZAMS)

shifted to brighter magnitudes by 0.75 mag. The locus obtained for NGC 362 is shown as

a red dashed line in Figure 16. As can be seen, red BSS lie in a sparse area adjacent to

the lower boundary in a region that we can call the MT-BSS domain (highlighted in grey

in Figure 16). It is particularly interesting to note that 3, out of the 4 WUMa candidates

discovered in this work, lie along the red sequence where MT-BSS are expected.

In F09, the presence of two distinct sequences of BSS has been connected to the dy-

namical state of M 30, in particular to the fact that this cluster might have recently (1 − 2

Gyr ago) experienced the collapse of the core. As discussed in Section 3, the dynamical state

of NGC 362 is quite debated, and controversial results are found in the literature (Fischer

et al. 1993; Trager et al. 1995; McLaughlin & van der Marel 2005). The density profile

cusp (α ∼ −0.2) discussed in Section 3 is shallower than typically observed in PCC clusters

and could indicate that NGC 362 is on the verge or is currently experiencing the collapse

– 18 –

of the core (Vesperini & Trenti 2010). The advanced dynamical age of NGC 362 is also

suggested by its monotonic BSS radial distribution. In fact, in the ”dynamical clock” classi-

fication (F12), NGC 362 belongs (with M 30) to the family of the highly dynamically-evolved

clusters (Family III).

On the basis of this observational evidence we can argue that also in the case of NGC 362

the presence of a double BSS sequence could be connected to the advanced dynamical state

of the cluster. As in the case of M 30, the fact that we observe two distinct sequences, and

in particular a well defined blue one, implies that the event that triggered the formation of

the double sequence is recent and short-lived. If this event is connected with the dynamical

evolution of the system, it could likely be the collapse of the core (or its initial phase). Indeed,

during the collapse, the central density rapidly increases, also enhancing the probability of

gravitational encounters (Meylan & Heggie 1997): thus, blue BSS could be formed by direct

collisions boosted by the high densities reached in the core, while the red BSS population

could have been incremented by binary systems brought to the mass-transfer regime by

hardening processes induced by gravitational encounters (McMillan, Hut & Makino 1990;

Hurley et al. 2008).

Quite interestingly, the red and the blue BSS show different radial distributions in

both M 30 and NGC 362. The origin of this feature still remains not completely clear.

If the collapse of the core played a role in the origin of the two sequences, then it could

also have had an impact on setting their radial distributions. While significant recoils are

expected both for collisional products and for hardened binaries, the fact that blue BSS are

more sparsely distributed might indicate that gravitational kicks are stronger in the former

case. Alternatively, most of the observed red BSS sank into the cluster center because of

dynamical friction and did not suffer significant hardening during the core collapse phase.

As a consequence, they did not experienced significant recoil and they appear more centrally

segregated than blue BSS (which have been, instead, kicked outwards during collisional

interactions). Within such a scenario the properties of the blue BSS suggest that the core

collapse occurred very recently (∼ 0.2 Gyr ago) and over a quite short time scale, of the

order of the current core relaxation time (∼ 108 yr; Harris 1996).

Indeed detailed spectroscopic investigations and accurate dynamical simulations are urged to

shed light on both the nature of the red and blue BSS sub-populations and their dynamical

properties.

This research is part of the project COSMIC-LAB (http://www.comic-lab.eu) funded

by the European Research Council (under contract ERC-2010-AdG-267675).

– 19 –

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This preprint was prepared with the AAS LATEX macros v5.2.

– 23 –

rint rext NBSS NSGB Lannsamp/L

totsamp

0′′ 13′′ 20 245 0.13

13′′ 50′′ 37 1066 0.39

50′′ 100′′ 8 423 0.16

100′′ 250′′ 9 473 0.24

250′′ 720′′ 3 191 0.08

Table 1: Number of BSS and SGB stars after field stars subtraction and fractions of sampled

light in the five radial annuli used to study the BSS radial distribution (Section 5.3)

– 24 –

Fig. 1.— Schematic map of the entire data-base used in this work with respect the position

of Cgrav (X0, Y0). The inset shows a zoomed view of the two HST sets of images. North is

up, East left.

– 25 –

Fig. 2.— Map of the HST WFC3 data-set with the position of the red and blue BSS

highlighted. The black cross marks the position of Cgrav. As in Figure 1, North is up, East

left.

– 26 –

Fig. 3.— CMDs of the three photometric samples used for the determination of the density

profile, the shaded regions delimit the stars included in the analysis (see Section 3).

– 27 –

Fig. 4.— Observed star count density profile as a function of radius (open grey squares).

The dotted line represents the density value of the background, obtained averaging the four

outermost points. Black filled dots are densities obtained after background subtraction (see

Section 3). The best mono-mass King model is also over-plotted to the observations (solid

line). The structural parameters are labelled. The lower panel shows the residuals between

the observations and the best-fit model. The inset shows a zoom on the innermost portion

of the profile. The dashed line marks the power-law fitting the central cusp, while the dotted

line represents the additional King model used to reproduce the innermost ∼ 3′′.

– 28 –

Fig. 5.— Upper panels. In the leftmost panel VPDs in pixel/yr of all the stars identified in

common between the first and second epoch (see Section 4). In the middle panel the cluster

and the SMC populations are selected in black and red respectively. In the rightmost panel

only cluster member are selected. Lower panels. From left to right, (V,U-I) CMDs for all

the detected stars, for stars with a high cluster membership probability and SMC selected

stars (red dots), and for cluster members only.

– 29 –

Fig. 6.— On the left (V,V-I) CMD of stars in the WFC3 FoV. In black stars selected

according to their membership probability, in grey stars excluded on the basis of the criteria

highlighted in the VPDs in the right panels. On the right, VPDs at different magnitude

levels. The distribution of stars gets broader moving to very faint and bright magnitudes

because of the uncertainties on the centroid determination. The black circle represent the

2σ fiducial region used to clean our sample from non-member stars.

– 30 –

Fig. 7.— A zoomed view of the (V,V-I) CMD of NGC 362 on the BSS region. BSS are

highlighted as red and blue symbols, and the photometric errors are shown as error bars.

The grey areas are represent the fiducial loci of the red BSS and blue BSS of M 30 (from

F09). Open squares are SX-Phoenicis found by Szekely et al. (2007). Open pentagons and

filled triangles are respectively SX-Phoenicis and WUMa stars identified in this work. Grey

crosses are stars excluded for saturation or non linearity problems.

– 31 –

Fig. 8.— Upper panel. Histogram of the distances (d) of red BSS (red area) and blue

BSS (blue area) of NGC 362 in the (V,V-I) CMD from the same reference line used in

F09 and passing through the blue sequence. For comparison we superimposed the distance

distribution of the BSS in M 30 (grey shaded histogram). Lower panel. Histogram of

distances for the combined sample of BSS observed in M 30 and NGC 362.

– 32 –

Fig. 9.— Cumulative radial distribution of the red and blue BSS samples. In black the

distribution of SGB stars, taken as reference population. This analysis is limited to the

WFC3 FoV which extends to a distance from Cgrav r ∼ 100′′, corresponding to about 8−9rc.

– 33 –

Fig. 10.— Light curves folded to the best period solutions (obtained as described in Sec-

tion 5.2) of the four candidates WUMa CWUMa identified in this work.

– 34 –

Fig. 11.— As for Figure 10 for the three candidate SX-Phoenicis identified in this work.

The black lines are the best-fit obtained for each light curve in each band with GRATIS.

– 35 –

Fig. 12.— Left panel: (V, B-V) CMD of the WFI sample for the stars with 100′′ < r < 720′′.

Open circles are the selected BSS, open triangle are selected SGB stars. Right panel WFI

CMD of the control field at r > 900′′. The objects lying with the BSS and SGB selection

boxes have been counted and used to estimate the Galactic field contamination.

– 36 –

Fig. 13.— Upper panel: radial distribution of the specific frequency NBSS/NSGB as a function

of the distance from Cgrav normalized to rc. Lower panel: radial distribution of the double

normalized ratio of BSS and SGB.

– 37 –

Fig. 14.— Radial distribution of the BSS double normalized ratio of NGC 362 compared to

that of the other clusters grouped in Family III by Ferraro et al. (2012). The distribution in

NGC 362 well resembles that of M 75 and M 79, decreasing less rapidly than that of other

(more evolved) clusters in this group. NGC 362 also shows the smallest central peak value

(RBSS ∼ 2) within in this family.

– 38 –

Fig. 15.— ”Dynamical clock” plot: relaxation time at the cluster center normalized to the age

of the Universe tH as a function of the time-hand of the dynamical clock, log(rmin/rc). Black

arrows are the lower limits of the minimum position for Family I clusters. Filled circles are

Family II members, while grey triangles are Family III clusters. The black triangle highlights

the position of NGC 362.

– 39 –

Fig. 16.— As in Figure 7, the grey shaded area (here defined as “MT-BSS domain”) ap-

proximately indicates the region populated by mass-transfer binaries in M 67 (Tian et al.

2006), ”translated” into the CMD of NGC 362. The solid black line is a 0.2 Gyr collisional

isochrone (Sills et al. 2009).